Question

The faces of a red cube and a yellow cube are numbered from 1 to 6. Both cubes are rolled. What is the probability that the top face of each cube will have the same number?

Answer 1

Total no. of outcomes when both cubes are rolled = 6×6 = 36 which are

{ (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) }

E ⟶ event of getting same no. on each cube

No. of favourable outcomes = 6 which are

{ (1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6)}

Probability, P(E) = (No.of favorable outcomes)/(Total no.of possible outcomes) = 6/36 = 1/6